Wittgenstein was a very important philosopher of the early twentieth century. One of his most important points was that which has been known as the Private Language Argument. This argument was given a new interpretation by Saul Kripke in 1982, which stirred up much debate. This essay investigates Kripke´s so called “skeptical challenge” and his “skeptical solution” to that challenge. To further enlighten the subject this essay also discusses a critique to Kripke´s interpretation, provided by the main critics, Baker and Hacker (1984). The conclusion of the essay is that Kripke´s theory takes up some interesting and important issues, although there are some serious flaws in Kripke´s solution that needs to be addressed if the solution is to be taken seriously.